Question

Math

Posted 4 months ago

```
Factor.
$2 z^{2}-17 z+35$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

We start by factoring the quadratic expression $2z^2 - 17z + 35$

step 2

We look for two numbers that multiply to $2 \cdot 35 = 70$ and add up to $-17$. These numbers are $-7$ and $-10$

step 3

Rewrite the middle term using these numbers: $2z^2 - 7z - 10z + 35$

step 4

Factor by grouping: $z(2z - 7) - 5(2z - 7)$

step 5

Factor out the common term: $(2z - 7)(z - 5)$

Answer

$(2z - 7)(z - 5)$

Key Concept

Factoring Quadratics

Explanation

To factor a quadratic expression, we look for two numbers that multiply to the product of the leading coefficient and the constant term, and add up to the middle coefficient. We then use these numbers to split the middle term and factor by grouping.

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